Does Noodles naively ignore the reality about Max's betrayal?
No, Noodles does not ignore the reality, he just consciously chooses to ignore it. And in order to understand this choice one must remember how he got to the final confrontation with Max.
Upon receiving the letter that calls him back to New York after 35 years ("of going bed early" in the words of Noodles himself) of hiding and laying low, he's aware that someone from the past has finally found him.
He's suspicious about the reason (could be an old enemy) and he's still wondering who is the person that sent him the "invitation", although he's sure that is someone that knows him well. Throughout the movie Noodles starts finding clues that leads him, towards the end of the film, to her ex lover Deborah, which he found out to be the mistress of Senator Bailey, the man that has sent Noodles a mysterious invitation to his mansion for a party.
Deborah warns Noodles about going to the Senator's party and also about meeting his son, who's waiting for her outside the dressing room of the theatre where Noodles and Deborah are meeting:
DEBORAH - "We're both old. All we have left are a few memories.
If you go to that party, you won't even have them any more.
Tear up that invitation. [...] I'm begging you Noodles"
NOODLES - "Are you afraid I'll turn into a pillar of salt?"
DEBORAH - "If you go out that door, yes."
But Noodles is determined to find out the truth after all this time:
DEBORAH - "This is the son of Senator Bailey. His name is David. The same as yours"
and so he finds himself in front of his young friend Max, as if 35 years didn't pass. Although it is not revealed out loud in the movie, it is perfectly plausible to imagine that Noodles has finally understood who is waiting for him at the party and who this Senator Bailey actually is. He could tear up the invitation, as Deborah suggested, but after all he's learned he can't go back to his life without a final encounter with his old friend.
At the party Senator Bailey doesn't waste much time dwelling on the past with Noodles and, since he will be dead anyway in a matter of days, he goes straight to the point and tries to manipulate Noodles into killing him by urging Noodles to exact his revenge and reminding him that:
MAX - "I ruined your life, Noodles. For forty years, I've let you think you got me killed. Your eyes were too full of tears to see it wasn't me lying burned up on the street. [...] I took your whole life away from you; I've been living in your place. I took everything - your money, your girl... What are you waiting for?"
But Noodles has a much simpler version of the story:
NOODLES - "Many years ago I tried to save a friend of mine by turning him in. He was a very close friend. Things worked out bad for him and for me."
and he sticks to it. To deny what has happened, what he believed for 35 years has happened, it would also mean for him to acknowledge that all the grief and the remorse for causing the death of his friends (Max, Patsy and Cockeye) has been wasted. That all his life has been wasted. That the friendship in which he believied in up to this moment probably never existed.
Noodles walks away from Senator Bailey not because that's his way of taking revenge against him but because he believes that Max, his friend Max, died 35 years ago. This crooked politician standing in front of him is no one for Noodles and he has no grudge, no debt to exact from him.